Dimensions: Flatland

As we live in a three-dimensional world, it is difficult to imagine that there are higher dimensions. To illustrate this, the thought experiment of the hypothetical “Flatland" can be considered. Let us assume that there is a two-dimensional world called Flatland. Here, the concept of depth does not exist. Only forwards, backwards, left and right exist; there is no up and down. Everything that happens here would look like it was drawn on paper. 

Now let us interact with Flatworld. If we were to touch Flatworld with our finger, it would be like poking your finger through a newspaper. The inhabitants of Flatworld would see a circle suddenly appear out of nowhere that grows larger and larger. A person would appear as if they were being seen through a CT scanner - in sections. The concept that things can be above or below would sound crazy to a Flatlander, even though to us it appears as a simple concept. 

Let us take an ant walking along a piece of paper as an example of a “2D object”. If the ant wishes to go from one edge of the paper to the opposite edge, it must walk along the 2D plane. However, with our 3D powers, we can fold the paper into a cylinder; now the ant can walk to the other point in an instant (across the fold). To another ant on the other side, the ant would look as if it teleported and suddenly appeared out of nowhere. 

In another experiment, we make a Mobius strip (a ribbon is twisted once then its two sides are joined) and make an ant walk along it. Although the ant would think that it was walking in a straight line along a two-dimensional surface, it would have walked on both sides of the strip - a three-dimensional concept. If the Mobius strip concept is confusing, think of a garden hose instead: an ant walking along a straight garden hose is walking in: 1D (straight line), 2D (hose is actually a flat surface) and 3D (the ant can walk in a corkscrew pattern along the hose). 

If we were to tell that ant that it had just travelled in a higher dimension, that ant would either scoff at us or be genuinely terrified of the experience. To it, we (or the giant pink circle that it sees our finger as) would look like some omnipotent being that can see everything going on in its world and teleport from one place to another. And although the concept of depth would initially intimidate the ant, it would bring the level of the ant’s understanding of the world up one dimension. For if we see what we only know, then how can anyone see anything new? The only way to truly learn and understand new things would be to jump out of the box and see everything from the outside - just like an ant seeing the piece of paper it was on from a higher ground.

Although we may laugh at the foolishness of the Flatlanders (and the ant), to a being of the 4th dimension, we would appear just as stupid and naive. By applying what we learned from the world of Flatland to our three-dimensional world, we can expand our horizon of knowledge and understand what the fourth-dimension is.

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  1. jinavie posted this